On the Kinematic Reconstruction of Deep Inelastic Scattering at HERA: the $\Sigma$ Method

TL;DR

This paper introduces the $\Sigma$ method for reconstructing deep inelastic scattering variables at HERA, enabling precise measurement of the proton structure function $F_2(x,Q^2)$ especially in low x-low$Q^2$ regions with minimal systematic errors.

Contribution

The paper presents a new $\Sigma$ method for kinematic reconstruction in deep inelastic scattering, improving accuracy and reducing errors in structure function measurements.

Findings

$\Sigma$ method allows measurement in low x-low$Q^2$ region.

Compared $\Sigma$ method with existing methods, showing advantages.

Discussed effects of QED radiation on measurements.

Abstract

We review and compare the reconstruction methods of the inclusive deep inelastic scattering variables used at HERA. We introduce a new prescription, the $\Sigma$ method, which allows to measure the structure function of the proton $F_2(x,Q^2)$ in a large kinematic domain, and in particular in the low x-low$Q^2$ region, with small systematic errors and small radiative corrections. A detailed comparison between the $\Sigma$ method and the other methods is shown. Extensions of the $\Sigma$ method are presented. The effect of QED radiation on the kinematic reconstruction and on the structure function measurement is discussed.